If you read the article you will see that they aren't sure if there were people going from Polynesia to South America, or from South America to Polynesia. Or it could have been both ways.

For clarification, jeffreyrogers correctly states that the HN headline, based on the NYTimes subtitle "A new genetic study suggests that Polynesians made an epic voyage to^ South America 800 years ago", is wrong. As "irrational" points out, an epic journey did occur but we don't know the direction. To^ shouldn't be in the headline. Neither should "from".

The Polynesians are proven navigators but the natural current from Columbia/Ecuador to eastern Polynesia makes the alternative path quite plausible as demonstrated by Thor Heyerdahl's 1947 Kon-Tiki expedition.